The reason for the difference in behavior between the tunnelling probability and the decay probability lies in the underlying physical processes involved.
Tunnelling is a quantum mechanical phenomenon where a particle has a finite probability of passing through a classically forbidden barrier or potential energy barrier. This effect arises due to the wave-like nature of particles, as described by the Schrödinger equation. When a particle encounters a barrier, there is a certain probability that it can tunnel through it and appear on the other side. However, as the barrier becomes wider or higher, the probability of tunnelling decreases exponentially. This is why the tunnelling probability can approach zero as the barrier becomes increasingly insurmountable.
On the other hand, decay refers to the spontaneous transformation of a particle or nucleus into one or more different particles. In the context of radioactive decay, atoms have a certain probability of undergoing decay within a specific time interval. This probability is governed by the decay rate, which is related to the half-life of the radioactive substance. The decay probability does not reach zero because, in principle, there is always a finite probability for an unstable particle or nucleus to decay. However, this probability may be extremely low, leading to long half-lives for certain radioactive substances.
The difference between tunnelling and decay lies in the nature of the barriers involved. Tunnelling involves particles encountering potential energy barriers, while decay involves the inherent instability of certain particles or nuclei. Tunnelling probabilities decrease rapidly with increasing barrier strength, while decay probabilities may be extremely small but not truly zero.
It's important to note that both tunnelling and decay are quantum mechanical phenomena, and their behavior is described by probabilistic laws rather than deterministic ones. This probabilistic nature is a fundamental aspect of quantum mechanics and reflects the inherent uncertainties associated with the behavior of particles at the quantum scale.